In a large skillet, melt the butter. Add the red cabbage and cook over moderately high heat, tossing, until slightly wilted, 5 minutes. Add the vinegar and sugar. Season with salt and pepper. Add 1 cup of water, cover and cook over moderately low heat, stirring, until tender, 20 minutes. Uncover and cook until the liquid has evaporated, 5 minutes.
In a medium saucepan, combine the lentils and garlic with 3 cups of water and season with salt. Simmer over moderately low heat until the lentils are just tender, about 15 minutes. Drain, reserving 1/4 cup of the cooking liquid; discard the garlic. Wipe out the saucepan.
Melt the butter in the saucepan. Add the scallions and cook over moderate heat until softened, about 2 minutes. Add the lentils, vinegar and the reserved 1/4 cup of cooking liquid and cook until thickened slightly, about 1 minute longer. Stir in the olive oil and season with salt and pepper.
In a bowl, whisk the mayonnaise with the sour cream and vinegar. Stir in the green cabbage and season with salt and pepper.
Arrange the rye on a work surface and cut each slice into thirds. Spread with mustard and top with the pastrami. Spoon each topping onto 8 pastrami toasts and serve.